<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html> I think it was John Hartman that asked me for a drawing of what I meant about the key ratio changing depending on the starting position and ending position. Again, here is that exagerated example of the three points on the key. A is the key front, B is the capstan, and O is the fulcrum. And remember we are looking at the change in vertical position for points A and B. This drawing was done on a shareware CAD program. One triangle was drawn with coordinants that gave a triangle 15 units across (A2 B2) 14,14 units down (A2, O), and 11.18 down (B2, O). Two circles were then drawn, both with O as their center, one with a radius of 14.14, the other with a radius of 11.18. Then the triangle was rotated at copied at both 5 degrees, and -5 degrees from the origional (A2,B2,O). The net change in vertical position for the front of the key compared to the back of the key gave the following two ratios A3,B3 moved to A2,B2 yielded a 0.511 ratio A2,B2 moved to A1,B1 yeilded a 0.436 ratio This is kind of easy to see from an intuitive perspective if you just look at the diagram a bit and follow the << Key >> as it traces the two arcs. You can prove this using some basic trig as well if you like. In anycase, defining the arms of the key as key top front, down to balance rail bottom, up again to capstan top results in this same tendancy for the change in vertical position of the capstan compared to the key front. Tho of course due to the dimensions of a real key the difference in vertical ratio is not nearly as pronounced.. but just so. Tilting the key backwards (front up) increases the vertical rise of the capstan for the same degree of movement at the front of the key. Cheers RicB   <img SRC="cid:part1.3EE64791.B905990@grieg.uib.no" height=460 width=547>   -- Richard Brekne RPT, N.P.T.F. UiB, Bergen, Norway <a href="mailto:rbrekne@broadpark.no">mailto:rbrekne@broadpark.no</a> <a href="http://home.broadpark.no/~rbrekne/ricmain.html">http://home.broadpark.no/~rbrekne/ricmain.html</a> <a href="http://www.hf.uib.no/grieg/personer/cv_RB.html">http://www.hf.uib.no/grieg/personer/cv_RB.html</a>  </html>